Index: Difference-in-Differences

Difference-in-Differences

Routing Summary

This folder covers staggered/multi-period Difference-in-Differences, centered on Callaway & Sant’Anna (2020). Six interconnected notes on the group-time ATT framework, its assumptions, doubly-robust estimands, aggregation schemes, and simultaneous inference.

• Need the big picture, the three-step framework, or the TWFE critique? → Difference-in-Differences with Multiple Time Periods - Overview
• Need the disaggregated building block $ATT(g,t)$ and notation? → Group-Time Average Treatment Effects
• Need parallel trends, no-anticipation, or overlap conditions? → Identifying Assumptions for Staggered DiD
• Need the OR / IPW / doubly-robust identification (Theorem 1) and estimators? → Doubly-Robust Estimands for ATT(g,t)
• Need event-study / group / calendar / overall ATT aggregation? → Aggregating Group-Time Effects
• Need asymptotics, the multiplier bootstrap, uniform bands, or the minimum-wage results? → Simultaneous Inference via Multiplier Bootstrap

Concept Map

Concept	Note	Type	Depends On	Key Result
Three-step framework & TWFE critique	Difference-in-Differences with Multiple Time Periods - Overview	overview	The Experimental Ideal; Difference in differences	Separate identify→aggregate→infer bypasses TWFE negative weights
Group-time ATT building block	Group-Time Average Treatment Effects	concept	Overview; Estimands in Longitudinal Research	$ATT(g,t)=\mathbb{E}[Y_t(g)-Y_t(0)\mid G_g=1]$, no heterogeneity restriction
Identifying assumptions	Identifying Assumptions for Staggered DiD	definition	Group-Time ATT; DAGs	Limited anticipation (A3) + conditional parallel trends (A4/A5) + overlap (A6)
OR / IPW / DR identification	Doubly-Robust Estimands for ATT(g,t)	theorem	Identifying Assumptions; Group-Time ATT	Theorem 1: three equivalent estimands; reference period $g-\delta -1$
Aggregation schemes	Aggregating Group-Time Effects	concept	Group-Time ATT; DR Estimands	$\theta =\sum w(g,t)ATT(g,t)$: event-study, group, calendar, overall
Asymptotics & multiplier bootstrap	Simultaneous Inference via Multiplier Bootstrap	theorem	DR Estimands; Aggregation	Thm 2–3, Cor 1: uniform bands; min-wage application

Notes

• Difference-in-Differences with Multiple Time Periods - Overview — CONTAINS: staggered-adoption problem, the static/dynamic TWFE critique (Goodman-Bacon, Sun-Abraham, de Chaisemartin-D’Haultfœuille), the identify→aggregate→infer framework, R did package, minimum-wage headline result.
• Group-Time Average Treatment Effects — CONTAINS: full setup/notation (group $G$, never-treated $C$, $\bar{g}$, generalized propensity score $p_g(X)$), Assumptions 1–2 (irreversibility, random sampling), potential-outcomes Eq. (2.1), definition of $ATT(g,t)$, why it avoids TWFE bias.
• Identifying Assumptions for Staggered DiD — CONTAINS: Assumption 3 (limited anticipation, horizon $\delta$), Assumption 4 (conditional parallel trends, never-treated), Assumption 5 (conditional parallel trends, not-yet-treated), Assumption 6 (overlap), conditional-vs-unconditional discussion, Roth (2020) no-pre-testing warning.
• Doubly-Robust Estimands for ATT(g,t) — CONTAINS: OR (2.3), IPW (2.2), DR (2.4) estimands + not-yet-treated analogues (2.5–2.7), Theorem 1 (nonparametric identification, both comparison groups), unconditional collapse (2.8–2.9), Remarks 3–4 TWFE-is-not-ATT(g,t), Hájek DR plug-in estimators (4.1–4.2).
• Aggregating Group-Time Effects — CONTAINS: general weighting (3.1), event-study ${\theta }_{es}(e)$ (3.4) + composition decomposition (3.5) + balanced ${\theta }_{es}^{bal}$ (3.6), group-specific ${\theta }_{sel}(\tilde{g})$ (3.7), calendar-time ${\theta }_c$/${\theta }_c^{cumu}$ (3.8–3.9), overall ${\theta }_W^O$ (3.10) and recommended ${\theta }_{sel}^O$ (3.11), Table 1 weights, equality-only-under-homogeneity result.
• Simultaneous Inference via Multiplier Bootstrap — CONTAINS: Theorem 2 (DR influence function, joint normality, Assumptions 7–8), Theorem 3 + Mammen weights + bootstrap draw (4.6), Algorithm 1 (studentized simultaneous band), Corollary 1 (uniform coverage), Corollary 2 (summary-parameter inference), Remark 12 (pre-treatment placebos), and the full minimum-wage empirical findings (Tables 2–3, Fig. 1).

Sources

• 1803.09015-Callaway-SantAnna-DiD-Multiple-Periods.pdf — Callaway & Sant’Anna (2020), “Difference-in-Differences with Multiple Time Periods,” Journal of Econometrics. JEL C14, C21, C23, J23, J38. 45 pp. Open-source R package did (CRAN). Supplementary Appendix at pedrohcgs.github.io.

See Also

• Identification Strategies — IV, RD, synthetic control, and the canonical DiD
• Synthetic Control — alternative for staggered policy adoption
• Difference in differences — PyMC Bayesian DiD tutorial (2x2 baseline)
• Mostly Harmless Econometrics — DiD chapter (Angrist & Pischke)
• The Experimental Ideal — randomization benchmark
• Estimands in Longitudinal Research — choosing potential-outcome targets